The number one benefit that Gmail touted when it launched was searchable email. That will break.
You're perfectly free to use E2E encryption on Gmail, and they are even trying to make it easy for you, though that project is evidently not as well staffed as the advertising org.
The inverted index could simply be built/live on client side. The cloud is then just a backup data storage. Encrypted email is downloaded, unencrypted and indexed on your laptop/phone etc.
